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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## Operation on rational numbers tagged by: Brent@GMATPrepNow ##### This topic has 4 expert replies and 2 member replies ## Operation on rational numbers An OG question Q. At a loading dock, each worker on the night crew loaded 3/4 as many boxes as each worker on the day crew. If the night crew has 4/5 as many workers as the day crew, what fraction of all the boxes loaded by the two crews did the day crew load? (A) 1/2 (B) 2/5 (C) 3/5 (D) 4/5 (E) 5/8 Don't really follow the explanation given in the OG. ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 14881 messages Followed by: 1855 members Upvotes: 13060 GMAT Score: 790 Quote: At a loading dock, each worker on the night crew loaded 3/4 as many boxes as each worker on the day crew. If the night crew has 4/5 as many workers as the day crew, what fraction of all the boxes loaded by the two crews did the day crew load? (A) 1/2 (B) 2/5 (C) 3/5 (D) 4/5 (E) 5/8 Day crew: Let the number of workers = 5. Let the number of boxes loaded by each worker = 4. Total number of boxes loaded = 5*4 = 20. Night crew: Since the night crew has 4/5 as many workers as the day crew, the number of workers on the night crew = (4/5)5 = 4. Since each worker on the night crew loads 3/4 as many boxes as each worker on the day crew, the number of boxes loaded by each night crew worker = (3/4)4 = 3. Total number of boxes loaded = 4*3 = 12. (Boxes loaded by the day crew)/(Total number of boxes loaded by the two crews) = 20/(20+12) = 20/32 = 5/8. The correct answer is E. _________________ Mitch Hunt Private Tutor for the GMAT and GRE GMATGuruNY@gmail.com If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Student Review #1 Student Review #2 Student Review #3 Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now. ### GMAT/MBA Expert Elite Legendary Member Joined 23 Jun 2013 Posted: 9892 messages Followed by: 491 members Upvotes: 2867 GMAT Score: 800 HI saadishah, TESTing VALUES (the approach that Mitch used) is a fairly easy way to work through this question. If you want to use an Algebraic approach, then that's fine, but you have to be very careful about what your variables represent. The number of night workers is related to the number of day workers... IF... N = number of night workers D = number of day workers N = (4/5)D Next, you have to create a variable and an equation for the number of boxes loaded per employee. B = number loaded per day worker (3/4)B = number loaded per night worker Now we can set up a ratio of boxes loaded by the Day workers to TOTAL boxes loaded by all workers: (D)(B) / [ (D)(B) + (N)(3/4)(B) ] Since N = (4/5)D, we can substitute in that value... DB / [DB + (4/5)(D)(3/4)(B)] Next, we can multiply and simplify... DB / [DB + (12/20)DB] DB / (32/20)DB] 1 / [32/20] 20/32 = 5/8 Final Answer: E GMAT assassins aren't born, they're made, Rich _________________ Contact Rich at Rich.C@empowergmat.com ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12341 messages Followed by: 1243 members Upvotes: 5254 GMAT Score: 770 Quote: At a loading dock, each worker on the night crew loaded 3/4 as many boxes as each worker on the day crew. If the night crew has 4/5 as many workers as the day crew, what fraction of all the boxes loaded by the two crews did the day crew load? A. 1/2 B. 2/5 C. 3/5 D. 4/5 E. 5/8 I think the fast way is to plug in some nice numbers. Since the two pieces of information regarding the night shift are related to the information regarding the day shift, let's assign some nice values to the DAY shift. Number of workers Day shift: 5 workers (this is an easy number to find 4/5 of) Night shift: 4 workers (4/5 of 5 = 4) Boxes loaded per worker Day shift: 4 boxes per worker Night shift: 3 boxes per worker (3/4 of 4 = 3) Total boxes loaded Day shift: 5 workers times 4 boxes per worker = 20 boxes Night shift: 4 workers times 3 boxes per worker = 12 boxes Combined total boxes for both shifts = 20 + 12 = 32 Of the 32 boxes, the day shift loaded 20 of them. 20/32 = 5/8 Answer: E Cheers, Brent _________________ Brent Hanneson â€“ Creator of GMATPrepNow.com Use our video course along with Sign up for our free Question of the Day emails And check out all of our free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMATâ€™s FREE 60-Day Study Guide and reach your target score in 2 months! Newbie | Next Rank: 10 Posts Joined 12 Jan 2016 Posted: 2 messages saadishah wrote: An OG question Q. At a loading dock, each worker on the night crew loaded 3/4 as many boxes as each worker on the day crew. If the night crew has 4/5 as many workers as the day crew, what fraction of all the boxes loaded by the two crews did the day crew load? (A) 1/2 (B) 2/5 (C) 3/5 (D) 4/5 (E) 5/8 Don't really follow the explanation given in the OG. As given in the problem night crew loaded 3/4 boxes and there are 4/5 workers as compared to day crew, so in effect their work is 3/4 * 4/5= 3/5 times the day crew's work, which means the ratio of night crew's work to day crew's work is 3:5. That easily gives the fraction of work by day crew, i.e 5/(3+5) = 5/8. ### GMAT/MBA Expert GMAT Instructor Joined 09 Apr 2015 Posted: 1461 messages Followed by: 17 members Upvotes: 39 saadishah wrote: An OG question Q. At a loading dock, each worker on the night crew loaded 3/4 as many boxes as each worker on the day crew. If the night crew has 4/5 as many workers as the day crew, what fraction of all the boxes loaded by the two crews did the day crew load? (A) 1/2 (B) 2/5 (C) 3/5 (D) 4/5 (E) 5/8 We are given that the night crew loaded 3/4 as many boxes as each worker on the day crew and that the night crew has 4/5 as many workers as the day crew. 4/5 x (number of day workers) = number of night workers Let's choose the convenient value of 20 for the number of day workers and substitute it into the equation above: 4/5 x 20 = number of night workers 16 = number of night workers Next, we set up the equation for the number of boxes loaded by each worker. 3/4 x (number of boxes loaded by each day worker) = number of boxes loaded by each night worker Now let's choose the convenient value of 8 for the number of boxes loaded by each day worker and substitute it into the above equation: 3/4 x 8 = number of boxes loaded by each night worker 6 = number of boxes loaded by each night worker Thus, the total number of boxes loaded by each type of worker is as follows: Day workers = 20 x 8 = 160 Night workers = 16 x 6 = 96 Total boxes loaded = 160 + 96 = 256 The question asks us to determine the fraction of all the boxes loaded by the day crew, and that is: (Total boxes loaded by day crew)/(Total boxes loaded) 160/256 = 40/64 = 5/8 Answer: E _________________ Jeffrey Miller Head of GMAT Instruction Newbie | Next Rank: 10 Posts Joined 24 Sep 2018 Posted: 3 messages Day workers (20) Night workers (20) * (4/5) = 16 Number of boxes per day worker = 1 per worker so (20 ) total Number of boxes per night worker = (3/4)*(16) = 12 total for night worker combined day and night = 20 + 12 = 32 Day / combined = 20/32, simplified, divided the top and bottom by (4) Number of Workers for day 20/32 divided by 4/4 = 5/8 • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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